Improbability of collisions in Newtonian gravitational systems. II

Abstract

It is shown that the set of initial conditions leading to collision in the inverse square force law has measure zero. For the inverse q q force law the behavior of binary collisions for 1 > q > 3 1 > q > 3 and the behavior of any collision for q = 1 q = 1 is developed. This information is used to show that collisions are improbable in the inverse q q force law where q > 17 / 7 q > 17/7 and that binary collisions are improbable for q > 3 q > 3 .